In virtue of the recent flowering of historical interests among fom-ers,
maybe it's worth mentioning that the 15 November (2007) issue of "Nature"
has a review (by Brian Clegg) of "The Archimedes Codex" by Reviel Netz and
William Noel. The book is about the decipherment (not sure that's the right
word-- it wasn't in code, but the manuscript was a palimpsest and only
readable with fairly high-tech means of a recently discovered Greek
manuscript of a treatise by Archimedes. Of interesdt from our point of
view, the reviewer writes:
"Before the codex was deciphered, it was thought that,
apart from some playful consideration of true infinity by
Galileo Galilei, the concept was hardly touched on until
the nineteenth century. Netz painstakingly retrieves text
from the codex proposing that two infinite sets have the
same size because the elements in them can be put in a
one-to-one correspondence. Such sets are now said to have
the same 'cardinality', the modern concept that establishes
that two sets are equivalent in magnitude. Yet here was
Archimedes using this argument more than 2,000 years
before Georg Cantor added it into the mathematical armoury."
("true" infinity seems to be Clegg's word for actual inf.)
(For anyone reading this in the FOM archive in the distant future: "Nature"
volume 450, pp. 352-353.)
--
Allen Hazen
Philosophy Department
University of Melbourne